在這篇論文中,我們提出一個在無線感測網路環境下估測多訊號源的方法。我們把無線感測網路模擬成一個因子圖形，然後我們就可以收集到的資訊在FC利用和積演算法去估測出多訊號源.假設訊號源和雜訊都是高斯分佈，此時和積演算法就可以被稱為GaBP演算法.而此種演算法具備了特殊性質，想要更新傳送的整體訊息，只需要更新高斯分佈的平均值和變異數即可。如果在會收斂的情況下，我們就可以得最終的估測結果。但此種演算法的缺點就是當係數矩陣連線密度很高的時候不確保一定會收斂。我們提出的方法就是利用對角線元素特殊的收斂性質解決這類的問題適用於任意M乘N的係數矩陣.在我們提出確保收歛的方法之下，我們就可以利用GaBP演算法去估測並且徹底的避免任何可能發散的風險，並且我們會和MMSE 估測法比較其運算複雜度，當係數矩陣很稀疏的時候，利用Gabp的方式是可以大幅降低複雜度，並且達到相同的表現結果。我們會討論多種不同的連線機率和不同的矩陣大小，去觀察固定訊號源個數和固定感測器個數會帶來的影響，我們可以發現當感測器的數目固定，而訊號源的數量增加，會使我們原先的收斂機率下降，並且會有比較不良的估測結果。希望可以透過這篇論文，使得Gabp和無線感測網路的結合更加緊密，並且有效的提升收斂的機率還有係數矩陣密度很高的時候發散的問題。
In this work, we proposed a scheme for multi-source estimation using factor graph in wireless sensor network. We model the sensor networks as a factor graph, and we can use the sum-product algorithm to estimate the multiple sources. Assuming the distributions of source and observation noise are Gaussian, this kind of sum product algorithm is also called as the GaBP (Gaussian Belief propagation) algorithm. There is a special property for Gaussian, by updating the Gaussian mean and variance. We can get the final estimation if the GaBP algorithm converges. But the drawback of the GaBP algorithm is not has a convergence guarantee for highly connection of coefficient matrix. Our method is that using the diagonally dominant property to solve the problem for any coefficient matrix which size is M N. Under our proposed method, when we use the GaBP algorithm to estimate, we can totally avoid the risk of divergence.

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